Go to Vermillion City

Go to the house just north above the gym.  Go into the house, then to the back of it, where you will find
a trainer/rocket.

Team Rocket Grunt (Payoff: $554)

Pokemon (Level)   Type             Weakness(es)                            EXP
-------------------------------------------------------------------------------
Machop  (17)      Fighting         Flying, Psychic                         319
Drowzee (17)      Psychic          Bug, Dark, Ghost                        370

After you beat this chump, he will return the TM he stole.  This TM is TM28.
TM28 is dig.  Dig is an attack that hits on the second turn, and can also be
used to exit dungeons.  You are probably thinking you have to return this TM
but you do not!  You can keep it.  Anyways, continue heading south until you
are directly south of Cerulean City.  Hear go down even further into that tiny
house.  Go in this house, come through the escalator, and then go down to the
escalator that is leading up.  From here go around the patch of grass to the
trainer on the left.

Go to the house just west of the Pokemon
center, and get the old rod.  With this rod you can go fishing in almost any
area of water, but you won't find anything worthwhile.  (I think but I am not
sure the only Pokemon you can find with the Old Rod is Magikarp.

After you get the Old Rod, go south of Vermillion City.  After going a tad
south go west where there are two houses.  The house on the right has one
little midget inside it.  He'll ask you if you have a Spearow.  Then he will
ask you if you would like to trade it for his Farfetch'd.  If you have a
Spearow go ahead and trade it.  It will get you another Pokemon caught on your
dex, and another Pokemon seen on your dex.  If not you can always come back
later.

The house on the left has basically a Pokemon club inside of it.  Talk to the
old man on the chair to the left.  When he asks you if you have come to hear
about his collection of Pokemon say yes.  He will go on and on about his
Rapidash and then finish.  Because he has kept you so long, he will give you a
Bike Voucher.  Go all the way back to Cerulean City, and trade it in the bike
shop for your very own bike.  When you get your bike go to it on the Key items
slot and press register.  Now whenever you want to go cycling press select, and
bam your on your bike.